Reciprocal Formulation of the Modal Expansion Approach for Around-the-Corner Propagation in Street Canyons

In a recent paper, we have presented an efficient and simple approach to model electromagnetic propagation in urban street canyons, when both the transmitter and the receiver are below the rooftop level. The model is based on the modal expansion approach, and we have shown that it is computationally efficient and that it allows for deriving a straightforward expression of the average received signal strength. In that paper, the Line-of-Sight (LoS) propagation case was described and discussed in detail, and the complete derivation of results was provided. Conversely, for the Non-Line-of-Sight (NLoS) around-the-corner case, only the final results were presented and briefly discussed. In the present paper, first of all we provide full details on the derivation of formulas for the NLoS case. In addition, we extend the discussion of results and properly analyze the obtained NLoS propagation loss expression. Last but not least, in contrast with our previous propagation model, we here propose a new formulation of the NLoS case that satisfies a key property in electromagnetics, that is, reciprocity, which was previously fulfilled only in the LoS case. The presented models are validated using empirical models, ray-tracing algorithms, and experimental campaigns.